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Adaptive Boundary Element Method

Adaptive Boundary Element Method

Dirk Praetorius (ORCID: 0000-0002-1977-9830)
  • Grant DOI 10.55776/P21732
  • Funding program Principal Investigator Projects
  • Status ended
  • Start August 1, 2009
  • End July 31, 2014
  • Funding amount € 295,354
  • E-mail

Disciplines

Mathematics (90%); Physics, Astronomy (10%)

Keywords

    Boundary Integral Equations

Abstract Final report

For two reasons, fast and accurate error estimation plays a key role in reliable and efficient scientific computing: First, one may want to check whether the solution of a numerical simulation is accurate enough. Second, if this is not the case, one aims to improve the discretization, e.g., by local refinement of the underlying mesh. Both subjects are usually covered by so-called a posteriori error estimates and related adaptive mesh-refining algorithms. For error control in finite element methods (FEM), there is a broad variety of a posteriori error estimators available, and convergence as well as optimality of adaptive algorithms is well studied in the literature. This is in sharp contrast to the boundary element method (BEM), where only few a posteriori error estimators have been proposed. Moreover, even convergence of adaptive BEM is widely open. Finally, unlike the FEM, most a posteriori error estimators for BEM are computationally expensive and even implementationally challenging. The aim of the project is therefore threefold: First, to give a fair numerical comparison between the error estimators and adaptive mesh-refining algorithms proposed in the BEM literature. Second, to develop a posteriori error estimators in the context of BEM which are numerically cheap to compute. Third, to study the convergence and the optimality of associated adaptive algorithms.

For two reasons, fast and accurate error estimation plays a key role in reliable and efcient scientic computing: First, one may want to check whether the solution of a numerical simulation is accurate enough. Second, if this is not the case, one aims to improve the discretization, e.g., by local renement of the underlying mesh. Both subjects are usually covered by so-called a posteriori error estimates and related adaptive mesh-rening algorithms. For error control in nite element methods, there is a broad variety of a posteriori error estimators available, and convergence as well as optimality of adaptive algorithms is well studied in the literature. For integral equations, the funded research project derived a posteriori error estimates and developed and analyzed optimal adaptive mesh-renement strategies.

Research institution(s)
  • Technische Universität Wien - 100%
International project participants
  • Christoph Ortner, University of British Columbia - Canada
  • Norbert Heuer, Pontificia Universidad Catolica de Chile - Chile
  • Carsten Carstensen, Humboldt-Universität zu Berlin - Germany
  • Ernst Peter Stephan, Universität Hannover - Germany
  • Stefan Funken, Universität Ulm - Germany

Research Output

  • 1347 Citations
  • 66 Publications
Publications
  • 2014
    Title Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations
    DOI 10.48550/arxiv.1408.2693
    Type Preprint
    Author Feischl M
  • 2014
    Title Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor
    DOI 10.1515/cmam-2014-0019
    Type Journal Article
    Author Feischl M
    Journal Computational Methods in Applied Mathematics
    Pages 485-508
    Link Publication
  • 2013
    Title Novel inverse estimates for non-local Operators.
    Type Conference Proceeding Abstract
    Author Feischl M
    Conference Proceedings of IABEM 2013 Symposium of the International Association for Boundary Element Methods, Santiago de Chile
  • 2013
    Title Simple error estimators for the Galerkin BEM for some hypersingular integral equation in 2D
    DOI 10.1080/00036811.2012.661045
    Type Journal Article
    Author Erath C
    Journal Applicable Analysis
    Pages 1194-1216
  • 2013
    Title FEM-BEM couplings without stabilization.
    Type Conference Proceeding Abstract
    Author Feischl M
    Conference Proceedings of IABEM 2013 Symposium of the International Association for Boundary Element Methods, Santiago de Chile
  • 2013
    Title Convergence of adaptive FEM for some elliptic obstacle problem
    DOI 10.1080/00036811.2011.631916
    Type Journal Article
    Author Page M
    Journal Applicable Analysis
    Pages 595-615
  • 2017
    Title Local inverse estimates for non-local boundary integral operators
    DOI 10.1090/mcom/3175
    Type Journal Article
    Author Aurada M
    Journal Mathematics of Computation
    Pages 2651-2686
    Link Publication
  • 2015
    Title Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations
    DOI 10.1016/j.cma.2015.03.013
    Type Journal Article
    Author Feischl M
    Journal Computer Methods in Applied Mechanics and Engineering
    Pages 362-386
    Link Publication
  • 2015
    Title FEM–BEM coupling for the large-body limit in micromagnetics
    DOI 10.1016/j.cam.2014.11.042
    Type Journal Article
    Author Aurada M
    Journal Journal of Computational and Applied Mathematics
    Pages 10-31
    Link Publication
  • 2015
    Title Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements
    DOI 10.1002/num.22025
    Type Journal Article
    Author Feischl M
    Journal Numerical Methods for Partial Differential Equations
    Pages 603-632
    Link Publication
  • 2015
    Title Simultaneous quasi-optimal convergence rates in FEM-BEM coupling
    DOI 10.1002/mma.3374
    Type Journal Article
    Author Melenk J
    Journal Mathematical Methods in the Applied Sciences
    Pages 463-485
    Link Publication
  • 2015
    Title Quasi-optimal convergence rates for adaptive boundary element methods with data approx- imation - Part II: Hyper-singular integral equation.
    Type Journal Article
    Author Feischl M
  • 2015
    Title Energy norm based error estimators for adaptive BEM for hypersingular integral equations
    DOI 10.1016/j.apnum.2013.12.004
    Type Journal Article
    Author Aurada M
    Journal Applied Numerical Mathematics
    Pages 15-35
  • 2012
    Title Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity
    DOI 10.1007/s00466-012-0779-6
    Type Journal Article
    Author Aurada M
    Journal Computational Mechanics
    Pages 399-419
    Link Publication
  • 2012
    Title A posteriori error estimates for the Johnson–Nédélec FEM–BEM coupling
    DOI 10.1016/j.enganabound.2011.07.017
    Type Journal Article
    Author Aurada M
    Journal Engineering Analysis with Boundary Elements
    Pages 255-266
    Link Publication
  • 2016
    Title Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations
    DOI 10.1007/s10092-016-0190-3
    Type Journal Article
    Author Feischl M
    Journal Calcolo
    Pages 367-399
  • 2013
    Title Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods
    DOI 10.1515/cmam-2013-0010
    Type Journal Article
    Author Aurada M
    Journal Computational Methods in Applied Mathematics
    Pages 305-332
    Link Publication
  • 2013
    Title Quasi-optimal adaptive BEM.
    Type Conference Proceeding Abstract
    Author Feischl M
    Conference Proceedings of IABEM 2013 Symposium of the International Association for Boundary Element Methods, Santiago de Chile
  • 2013
    Title Each H1/2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd
    DOI 10.1051/m2an/2013069
    Type Journal Article
    Author Aurada M
    Journal ESAIM: Mathematical Modelling and Numerical Analysis
    Pages 1207-1235
    Link Publication
  • 2008
    Title Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
    DOI 10.1137/07069047x
    Type Journal Article
    Author Cascon J
    Journal SIAM Journal on Numerical Analysis
    Pages 2524-2550
    Link Publication
  • 2016
    Title Efficient numerical computation of direct exchange areas in thermal radiation analysis
    DOI 10.1080/10407790.2016.1173469
    Type Journal Article
    Author Feischl M
    Journal Numerical Heat Transfer, Part B: Fundamentals
    Pages 511-533
  • 2013
    Title On a decoupled linear FEM integrator for Eddy-current-LLG
    DOI 10.48550/arxiv.1306.3319
    Type Preprint
    Author Le K
  • 2013
    Title Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement
    DOI 10.1002/num.21792
    Type Journal Article
    Author Karkulik M
    Journal Numerical Methods for Partial Differential Equations
    Pages 2081-2106
  • 2013
    Title Convergence and Quasi-Optimality of Adaptive FEM with Inhomogeneous Dirichlet Data
    DOI 10.48550/arxiv.1306.5100
    Type Preprint
    Author Feischl M
  • 2013
    Title Each H^{1/2}-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in R^d
    DOI 10.48550/arxiv.1306.5115
    Type Preprint
    Author Aurada M
  • 2013
    Title On the Landau-Lifshitz-Gilbert equation with magnetostriction
    DOI 10.48550/arxiv.1303.4060
    Type Preprint
    Author Banas L
  • 2013
    Title ZZ-type aposteriori error estimators for adaptive boundary element methods on a curve
    DOI 10.48550/arxiv.1306.5120
    Type Preprint
    Author Feischl M
  • 2013
    Title HILBERT — a MATLAB implementation of adaptive 2D-BEM
    DOI 10.1007/s11075-013-9771-2
    Type Journal Article
    Author Aurada M
    Journal Numerical Algorithms
    Pages 1-32
    Link Publication
  • 2013
    Title Axioms of Adaptivity
    DOI 10.48550/arxiv.1312.1171
    Type Preprint
    Author Carstensen C
  • 2013
    Title L2-orthogonal projections onto finite elements on locally refined meshes are H1-stable
    DOI 10.48550/arxiv.1307.0917
    Type Preprint
    Author Karkulik M
  • 2013
    Title Optimal preconditioning for the symmetric and non-symmetric coupling of adaptive finite elements and boundary elements
    DOI 10.48550/arxiv.1311.5782
    Type Preprint
    Author Feischl M
  • 2013
    Title A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equation
    DOI 10.48550/arxiv.1303.4009
    Type Preprint
    Author Banas L
  • 2013
    Title Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, part I: weakly-singular integral equation
    DOI 10.1007/s10092-013-0100-x
    Type Journal Article
    Author Feischl M
    Journal Calcolo
    Pages 531-562
  • 2013
    Title Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method
    DOI 10.1137/110842569
    Type Journal Article
    Author Feischl M
    Journal SIAM Journal on Numerical Analysis
    Pages 1327-1348
  • 2013
    Title On 2D Newest Vertex Bisection: Optimality of Mesh-Closure and H1-Stability of L2-Projection
    DOI 10.1007/s00365-013-9192-4
    Type Journal Article
    Author Karkulik M
    Journal Constructive Approximation
    Pages 213-234
    Link Publication
  • 2013
    Title MIXED CONFORMING ELEMENTS FOR THE LARGE-BODY LIMIT IN MICROMAGNETICS
    DOI 10.1142/s0218202513500486
    Type Journal Article
    Author Aurada M
    Journal Mathematical Models and Methods in Applied Sciences
    Pages 113-144
  • 2012
    Title Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems
    DOI 10.1051/m2an/2011075
    Type Journal Article
    Author Aurada M
    Journal ESAIM: Mathematical Modelling and Numerical Analysis
    Pages 1147-1173
    Link Publication
  • 2012
    Title Convergence of adaptive FEM for some elliptic obstacle problem with inhomogeneous Dirichlet data
    DOI 10.48550/arxiv.1207.3257
    Type Preprint
    Author Feischl M
  • 2012
    Title Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics
    DOI 10.1007/s00211-012-0454-z
    Type Journal Article
    Author Ferraz-Leite S
    Journal Numerische Mathematik
    Pages 101-131
    Link Publication
  • 2012
    Title Estimator reduction and convergence of adaptive BEM
    DOI 10.1016/j.apnum.2011.06.014
    Type Journal Article
    Author Aurada M
    Journal Applied Numerical Mathematics
    Pages 787-801
    Link Publication
  • 2012
    Title Adaptive FEM with optimal convergence rates for a certain class of non-symmetric and possibly non-linear problems
    DOI 10.48550/arxiv.1210.8369
    Type Preprint
    Author Feischl M
  • 2012
    Title Convergence of adaptive BEM for some mixed boundary value problem
    DOI 10.1016/j.apnum.2011.03.008
    Type Journal Article
    Author Aurada M
    Journal Applied Numerical Mathematics
    Pages 226-245
    Link Publication
  • 2012
    Title Convergence of adaptive boundary element methods
    DOI 10.1216/jie-2012-24-1-1
    Type Journal Article
    Author Carstensen C
    Journal Journal of Integral Equations and Applications
    Pages 1-23
    Link Publication
  • 2012
    Title Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity
    DOI 10.48550/arxiv.1211.4225
    Type Preprint
    Author Aurada M
  • 2012
    Title Inverse estimates for elliptic boundary integral operators and their application to the adaptive coupling of FEM and BEM
    DOI 10.48550/arxiv.1211.4360
    Type Preprint
    Author Aurada M
  • 2012
    Title On 2D Newest Vertex Bisection: Optimality of Mesh-Closure and H1-Stability of L2-Projection
    DOI 10.48550/arxiv.1210.0367
    Type Preprint
    Author Karkulik M
  • 2012
    Title Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems
    DOI 10.48550/arxiv.1212.2620
    Type Preprint
    Author Feischl M
  • 2012
    Title Multiscale modeling in micromagnetics: existence of solutions and numerical integration
    DOI 10.48550/arxiv.1209.5548
    Type Preprint
    Author Bruckner F
  • 2011
    Title Convergence of adaptive FEM for elliptic obstacle problems
    DOI 10.1002/pamm.201110373
    Type Journal Article
    Author Feischl M
    Journal PAMM
    Pages 767-768
    Link Publication
  • 2011
    Title Adaptive coupling of FEM and BEM: Simple error estimators and convergence
    DOI 10.1002/pamm.201110367
    Type Journal Article
    Author Aurada M
    Journal PAMM
    Pages 755-756
  • 2011
    Title Residual a-posteriori error estimates in BEM: convergence of h-adaptive algorithms.
    Type Conference Proceeding Abstract
    Author Feischl M
    Conference Proceedings of IABEM 2011 Conference, Brescia
  • 2010
    Title Convergence of simple adaptive Galerkin schemes based on h - h/2 error estimators
    DOI 10.1007/s00211-010-0292-9
    Type Journal Article
    Author Ferraz-Leite S
    Journal Numerische Mathematik
    Pages 291-316
    Link Publication
  • 2014
    Title Multiscale modeling in micromagnetics: Existence of solutions and numerical integration
    DOI 10.1142/s0218202514500328
    Type Journal Article
    Author Bruckner F
    Journal Mathematical Models and Methods in Applied Sciences
    Pages 2627-2662
    Link Publication
  • 2014
    Title Adaptive FEM with Optimal Convergence Rates for a Certain Class of Nonsymmetric and Possibly Nonlinear Problems
    DOI 10.1137/120897225
    Type Journal Article
    Author Feischl M
    Journal SIAM Journal on Numerical Analysis
    Pages 601-625
    Link Publication
  • 2014
    Title Rate optimality of adaptive algorithms.
    Type Conference Proceeding Abstract
    Author Carstensen C
    Conference Proceedings of 11th World Congress on Compututational Mechanics (WCCM XI)
  • 2014
    Title Optimal preconditioning for the coupling of adaptive finite elements and boundary elements.
    Type Conference Proceeding Abstract
    Author Feischl M
    Conference Proceedings of 11th World Congress on Compututational Mechanics (WCCM XI), Barcelona
  • 2014
    Title Rate optimality of adaptive algorithms: An axiomatic Approach.
    Type Journal Article
    Author Carstensen C
    Journal ECCOMAS Newsletter
  • 2014
    Title A posteriori error estimation for adaptive IGA boundary element methods.
    Type Conference Proceeding Abstract
    Author Feischl M. Praetorius D Et Al
    Conference Proceedings of 11th World Congress on Compututational Mechanics (WCCM XI), Barcelona
  • 2014
    Title Stability of symmetric and nonsymmetric FEM–BEM couplings for nonlinear elasticity problems
    DOI 10.1007/s00211-014-0662-9
    Type Journal Article
    Author Feischl M
    Journal Numerische Mathematik
    Pages 199-223
  • 2014
    Title Axioms of adaptivity
    DOI 10.1016/j.camwa.2013.12.003
    Type Journal Article
    Author Carstensen C
    Journal Computers & Mathematics with Applications
    Pages 1195-1253
    Link Publication
  • 2014
    Title ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve
    DOI 10.1016/j.enganabound.2013.10.008
    Type Journal Article
    Author Feischl M
    Journal Engineering Analysis with Boundary Elements
    Pages 49-60
    Link Publication
  • 2014
    Title Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data
    DOI 10.1016/j.cam.2013.06.009
    Type Journal Article
    Author Feischl M
    Journal Journal of Computational and Applied Mathematics
    Pages 481-501
    Link Publication
  • 2014
    Title On a decoupled linear FEM integrator for eddy-current-LLG
    DOI 10.1080/00036811.2014.916401
    Type Journal Article
    Author Le K
    Journal Applicable Analysis
    Pages 1051-1067
    Link Publication
  • 2014
    Title Adaptive Boundary Element Methods
    DOI 10.1007/s11831-014-9114-z
    Type Journal Article
    Author Feischl M
    Journal Archives of Computational Methods in Engineering
    Pages 309-389
    Link Publication
  • 2011
    Title Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data
    DOI 10.1002/pamm.201110374
    Type Journal Article
    Author Feischl M
    Journal PAMM
    Pages 769-772
    Link Publication
  • 2011
    Title Efficient implementation of adaptive P1-FEM in Matlab
    DOI 10.2478/cmam-2011-0026
    Type Journal Article
    Author Funken S
    Journal Computational Methods in Applied Mathematics
    Pages 460-490
    Link Publication

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